at castle rock school 575 students ride their bikes to school. If this number is 92% of the school enrollment then how many students are enrolled?

The value of side b is 6.15

The value of side c is 6.84

The value of angle A is 26°

From the question, we are to determine the length of side b and c and the measure of angle A.

From the given information,

m ∠B = 64°

and

Angle C is a right angle.

We can write that

m ∠A + m ∠B + m ∠C = 180° (Sum of angles in a triangle)

m ∠A + 64° + 90° = 180°

m ∠A = 180° - 90° - 64°

m ∠A = 26°

From SOH CAH TOA, we can write that

tan B = b/a

tan 64° = b/3

b = 3 × tan 64°

b = 6.15

Also,

cos B = a/c

cos 64° = 3/c

c = 3/cos 64°

c = 6.84

Hence, the value of c is 6.84

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The mean, median and mode of the distance from home plate to the left-field fence  is 302.57 ft, 303 ft, 310 ftrespectively.

Mean is the sum of all values divided by the total number of values

To calculate the mean of the data given, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Also, to calculate the median of the distribution, we arrage the data into ascending or decending order.

Ascending order ⇒ 279, 297, 301, 303, 310, 310, 321

Then, the median is the middle term in the distribution

Finally to get the mode, we look for the term in the distribution that has the higest frequency.

Hence, the mean, median and mode is 302.57ft, 303 ft, 310 ft respectively

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The approximate percentage of daily phone calls numbering between 32 and 68 is 99.73

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using:

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (x - 50)/6

When x = 32, we have

z = (32 - 50)/6 = -3

When x = 68, we have

z = (32 - 50)/6 = 3

The percentage is then calculated as:

P(32 < x < 68) = P(-3 < z < 3)

From the z table of probabilities, we have;

From the z table of probabilities, we have;

P(32 < x < 68) = 0.99865 - 0.0013499

Evaluate

P(32 < x < 68) = 0.9973001

Rewrite as

P(32 < x < 68) = 99.73%

Hence, the percentage is 99.73%

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The volume of the cone is 91.05[tex]m^{3}[/tex]

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex. We can also define the cone as a pyramid which has a circular cross-section, unlike pyramid which has a triangular cross-section.

circumference of the base of a cone is same as circumference of a circle which is 2[tex]\pi[/tex]r

15.8 = 2[tex]\pi[/tex]r

make r subject of equation

r = [tex]\frac{15.8}{2\pi }[/tex]

r = 2.51m

Volume of a cone = 1/3 x [tex]\pi[/tex][tex]r^{2}h[/tex], but h =13.8m

volume = 1/3 x 3.142 x [tex](2.51)^{2}[/tex] x 13.8 which is 91.05[tex]m^{3}[/tex]

In conclusion the volume of the cone is 91.05[tex]m^{3}[/tex]

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The value y is -36.

Proportionality is the property of two variables being in a multiplicative relation to a constant.

Given that, y varies jointly with x and z and y=-60 when x=-5 and z=4,

y ∝ xz

Let k be the Proportionality constant,

y = kxz

-60 = k*4*-5

k = 3

When x = 4 and z = -3

y = 3*4*-3

y = -36

Hence, The value y is -36.

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Answer:

$13.50

Step-by-step explanation:

If the shirt is 10% off, that means the shirt is 90% of the original cost, which is $15.

If the shirt is 90% of the original cost which is 15, that means that we must turn the percentage into a decimal (0.9) and multiply it by 15.

0.9*15 = 13.5

The sale price of the shirt is $13.50

The value of s in the formula

[tex]s = ut + \frac{1}{2}at^2[/tex] is [tex]\frac{19}{4}[/tex]

What is subject of a formula?

At first, it is important to know about formula

Formula is an equation which consists of variables and numbers and they are connected by mathematical operations.

In a formula, there are many variables present.

Subject of a formula is that variable which can be expressed in terms of other variables present in the formula.

Here, s is the subject of the formula

[tex]s = ut + \frac{1}{2}at^2[/tex]

u = 10, a = -2, t = [tex]\frac{1}{2}[/tex]

s = [tex]10 \times \frac{1}{2} + \frac{1}{2}\times (-2) \times (-\frac{1}{2})^2\\[/tex]

s = [tex]5 - \frac{1}{4}[/tex]

s = [tex]\frac{20 - 1}{4}\\[/tex]

s = [tex]\frac{19}{4}[/tex]

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The volume of the pyramid will be 995,328 cubic meters.

Let h be the height of the pyramid, l be the slant height and A be the base area of the pyramid.

Then the volume of the pyramid will be

Volume = (1/3) × A × h

The slant height is given as.

l² = (half of the side)² + h²

A stone pyramid in Egypt has a square base that actions 144 m on each side. The level is 96 m.

Then the volume of the pyramid will be given as,

V = 1/3 x (144 x 144) x 96

V = 48 x 144 x 96

V = 995,328 cubic meters

The volume of the pyramid will be 995,328 cubic meters.

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Answer:

Step-by-step explanation:

27.5 percent of what is 13.75

13.75 : 27.5 * 100 =

(13.75 * 100) : 27.5 =

1375 : 27.5 = 50

The binary number (100[tex])_2[/tex] in decimal system is written as [tex]4_{10}[/tex].

Given:

Binary number = [tex](100)_2[/tex]

Converting Binary to decimal system:

Binary:

In computer applications, where binary numbers are represented by only two symbols or digits, i.e. 0 (zero) and 1(one).

Decimal:

Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.

[tex]100_2 = 1*2^2 + 0*2^1+0*2^0[/tex]

we know that,

[tex]2^0 = 1[/tex]

[tex]2^1 = 2\\2^2 =4[/tex]

substitute these values

[tex]100_2 = 1*4 + 0*2 + 0*1[/tex]

= 4 + 0 + 0

= 4 + 0

= [tex]4_{10}[/tex]

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Answer:

  g. x = -3, 1.875

  h. (-3, 1.875)

Step-by-step explanation:

You want the solutions to K(x) = -6 for K(x) -1.6x² -1.8x +3, and the interval for which K(x) > -6.

The attached graph shows K(x) = -6 for x = -3 and x = 1.875.

The attached graph shows K(x) > -6 between the above values, on the interval (-3, 1.875).

__

Additional comment

We are grateful that we are directed to use technology on this problem, as a graphing calculator makes answering these questions so much easier.

We know that  △ ABC ≅ △ DEF are congruent because AB corresponds to DE of another triangle, BC corresponds to EF and AC corresponds to DF.

According to the question,

We have the following information:

△ ABC ≅ △ DEF

Now, we know that this sign is used to show that the two triangles are congruent.

Now, we also know that in these two triangles, their corresponding sides will be equal. So, all the three sides of one triangle will be corresponding to the same sides in another triangle.

Hence, we know that  △ ABC ≅ △ DEF are congruent because AB corresponds to DE of another triangle, BC corresponds to EF and AC corresponds to DF.

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The balance in the account after 10 years is $15,384.45

From the question, we are to use the compound interest formula to compute the balance in the account

From the compound interest formula, we have that

A = P(1 + r/n)^nt

Where A is the amount

P is the principal

r is the interest rate

n is the number of times compounded per year

and t is the time.

From the given information,

P = $12,000

r = 5%= 0.05

n = 4

t = 10

Putting the parameters into the formula

A = P(1 + r/n)^nt

A = 12000(1 + 0.05/4)^(4×5)

A = 12000(1 + 0.0125)^20

A = $15,384.45

Hence, the balance is $15,384.45

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The equivalent rational expression of the given expression, 9/5u² - 40u - 45, is 9/(5u + 5)(u - 9)

The equivalent rational expression of the given expression, 2u/5u² + 30u + 25 , is 2u/(5u + 5)(u + 5)

From the question, we are to rewrite the given expressions as equivalent rational expressions.

The given expressions are:

9/5u² - 40u - 45 and 2u/5u² + 30u + 25

Writing an equivalent expression for 9/5u² - 40u - 45

Factorize the denominator

5u² - 40u - 45

5u² - 45u + 5u - 45

5u(u - 9) + 5(u - 9)

(5u + 5)(u - 9)

Thus,

The equivalent expression is 9/(5u + 5)(u - 9)

Writing an equivalent expression for 2u/5u² +30u + 25

Factorize the denominator

5u² +30u + 25

5u² +25u + 5u + 25

5u(u + 5) + 5(u + 5)

(5u + 5)(u + 5)

Thus,

The equivalent expression is 2u/(5u + 5)(u + 5)

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Answer:

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

                                   Hope this helps!

Answer:

[tex]\textsf{(d)} \quad \sf \dfrac{1}{5} < c < \dfrac{1}{3}[/tex]

(e)    p ≤ -5

(f)     -m ≥ -9

Step-by-step explanation:

Symbol notation

A negative real number is any real number that is less than zero.

A positive real number is any real number that is greater than zero.

Zero is neither positive nor negative.

[tex]\textsf{c is between $\dfrac{1}{5}$ and $\dfrac{1}{3}$}.[/tex]

If c is between 1/5 and 1/3, it is greater than 1/5 and less than 1/3 (as 1/5 < 1/3), but not equal to either number:

If p is not greater than -5, then it is less than or equal to -5:

If the negative of m is not less than -9, then it is greater than or equal to -9:

Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.

Given that,

We have to find what are the 2 characteristics of a regular polygon.

We know that,

Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.

Regular triangles and quadrilaterals are given unique names, such as squares and equilateral triangles.

Therefore, Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.

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The volume of the rectangular prism with length of 5 units, width of 4 units and height of 3 units is 60 unit³

An equation is an expression that is used to show the relationship between two or more numbers and variables.

Volume is the amount of space occupied by a three dimensional side or object.

Let us assume that the rectangle prism have length of 5 units, width of 4 units and height of 3 units. Hence:

Volume of prism = length * width * height

Volume = 5 units * 4 units * 3 units = 60 unit³

The volume is 60 unit³

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The statement "I have anywhere from $5 to $8 in my pocket." has been represented on the number line shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Translating the statement, we have the following inequality:

Let the variable x represent the amount of money in pocket.

From $5 to $8 in my pocket = 5 ≤ x ≤ 8.

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Answer:

Step-by-step explanation:

V = 16755.1608 m3

The I quadrant will contain the point (6, 8). The number is in the I quadrant as a result.

What is Quadrant?

A quadrant is any one of the four divisions of the coordinate plane. Additionally, we refer to the sections as they are divided by the coordinate axes when we talk about the sections. The y-axis is situated on this up-down axis, and the x-axis is situated here. As you can see, it divides the coordinate space into four parts.

A point can be mathematically expressed as:

A(x, y )

The intersection of the coordinate axes divides the cartesian plane into four quadrants (x and y-axis).

                        (x, y )

In the first quadrant, the x and y coordinates are both positive.

              (x, y)

Y is positive while x is negative in the second quadrant.

                      (-x, y)

The point will be located in the third quadrant if both x and y are equally negative.

                      (-x, -y)

The point will be located in the fourth quadrant if both x and y are positive.

                       (x, -y)

pointed out; A(6, 8)

The y-coordinate in the highlighted position is positive at (8), while the x-coordinate is negative at (6).

Remember that if the x-coordinate is negative and the y-coordinate is positive, the point is in the I quadrant.

As a result, the provided point (6, 8) is said to be in the I quadrant.

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If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

To comprehend the relationship between the rhombus shape, parallelogram, and square, look at the graphic below.

There are three additional names for a rhombus:

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The equations of the line are listed according to slope and intercept below:

According to Euclidean geometry, a line can be constructed by knowing the location of two different points set on Cartesian plane. From analytical geometry we find that lines are represented by an equation of the form:

y = m · x + b

Where:

The slope can be found by secant line formula:

m = Δy / Δx

Now we proceed to find the equation of the line for each case:

Case 1 - (x₁, y₁) = (3, 2), (x₂, y₂) = (5, 7)

m = (7 - 2) / (5 - 3)

m = 5 / 2

b = y - m · x

b = 2 - (5 / 2) · 3

b = 2 - 15 / 2

b = - 11 / 2

y = - (5 / 2) · x - 11 / 2

Case 2 - (x, y) = (- 3, 4), m = 2

b = y - m · x

b = 4 - 2 · (- 3)

b = 4 + 6

b = 10

y = 2 · x + 10

Case 3 - m = - 3, b = 5

y = - 3 · x + 5

Case 4 - x-intercept: 3, y-intercept: 0

m · 3 + b = 0

3 · m = - b

m · 0 + b = 0

b = 0

m = 0

y = 0

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The higher power of the polynomial equation is its degree when there is one variable. However, if a polynomial comprises numerous variables, the degree of the polynomial can be calculated by adding the powers of the multiple (more than one variable) variables in any terms in the polynomial expression.

Polynomial: A Polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

Examples:

•Constants. Example: 1, 2, 3, etc.

•Variables. Example: g, h, x, y, etc.

•Exponents: Example: 5 in x5 etc.

Degree of one variable polynomial:

Example: 4x^4+6x^2-2

The degree of the polynomial is 4 as the highest power of variable is 4.

Degree of more than two variables polynomial:

Example: 6x^2yz^3+2x^2y+zx

The degree of the polynomial is 6 as the addition of powers of variables is 6.

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The measure of the base BC in the given triangle is (C) 25 units.

A polygon with three edges and three vertices is called a triangle.

It is one of the fundamental geometric shapes.

The letter ABC stands for a triangle having the vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

If all of the geometry is in the Euclidean plane, then all triangles are encompassed in a single plane, however, in higher-dimensional Euclidean spaces, this is no longer the case.

This article concerns triangles in Euclidean geometry, specifically the Euclidean plane unless otherwise stated.

So, the given triangle is an isosceles triangle with AB = AC.

Then get the value of x as follows:

AB = AC

4x + 1 = 2x + 23

4x - 2x = 23 - 1

2x = 22

x = 22/2

x = 11

Now, substitute x = 11 in 3x - 8 that is BC.

3x - 8

3(11) - 8

33 - 8

25

Therefore, the measure of the base BC in the given triangle is (C) 25 units.

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Correct question:
What is the measure of the base in the triangle below?

a. 11

b. 45

c. 25

d. 30

Functions of the form  f(x)=kx represents direct variation.

The table of values that appears a constant proportion between two variables speaks to a direct variation function. In the event that there's at slightest one pair of values that features a different proportion, at that point the function isn't a direct proportion.  the equation applies to each corresponding value between the two variables. Functions of form f(x)=kx, where k is the constant, are as they were functions that can speak to a direct variation. Typically since direct proportion is spoken to by the direct variation formula that's given by. Functions of the form, there may be a constant, are the as it were functions that can speak to a direct variety. Typically since coordinate proportion is spoken to by the coordinate variation formula that's given by y=kx.

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The function of the graph is g(x) = [x]+2

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of terms

y = output variable

x = input variable

m = slope

c = y intercept

The c from the graph is +2

m for points (1, 3) and (-3, -1)

= (-1 - 3) / (-3 - 1)

= -4/-4

= 1

substituting to the equation  y = mx + c

y = x + 2

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The answer to this question is after solving definite integration 0,1,-4,-10

What is Definite integration?

It is just basically Simple Integration with limits. In other words it is completely same as area under curve

Solution:

We will proceed by finding area under curve

Here we have to consider the area above x axis as positive and area under x axis as negative area

In First part +ve area and -ve area cancels each other hence answer is 0

In second part after cancellation only 1 square block above x axis remains whose area is 1  hence answer is 1

remaining 2 parts graph is completely below x axis hene area is negative therefore definite integeration will be negative

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The five inequality symbols are greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol ().

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Answer:

Step-by-step explanation:

You want the equations of the lines parallel and perpendicular to y=-4x+4 through the points (-6, -4) and (-6, 4), respectively.

The equation of the given line is in slope-intercept form. This means its slope is the coefficient of x: -4.

Parallel lines have the same slope, so the parallel line will have slope -4.

Perpendicular lines have opposite reciprocal slopes, so the perpendicular line will have slope -1/(-4) = 1/4.

The point-slope equation of a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

This problem gives you a point on each line, and we know the required slope, so this form of the equation for a line is just what we need.

  m = -4, (h, k) = (-6, -4)

  y +4 = -4(x +6)

  m = 1/4, (h, k) = (-6, 4)

  y -4 = 1/4(x +6)